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The results of analyzing the data on strong М ≥ 5 earthquakes in Central Asia for 1901–2013 are presented. A statistical method for studying the influence of the strongest earthquakes in the region on the occurrence probability of seismic activation in a certain seismically active zone in Uzbekistan is used. Based on this method, the statistical significance of the difference between the fraction of strongest earthquakes in the region that fall within the alarm intervals of the studied seismically active zone and the fraction of cumulative time of alarms in this zone is assessed. It is established which seismically active zone in the Uzbekistan territory is most likely to manifest seismic activation if a strong earthquake occurs in the Central Asian region. A mathematical model is developed for the deformation of the Central Asia lithosphere, the lateral margins of which are being subjected to lateral compression. The proposed model is used to analyze changes in background stresses in the crust of Central Asia caused by strong earthquakes in the territory bounded by the geographical coordinates from 36° to 46° N and from 56° to 76° E. A numerical experiment is carried out by solving the inverse problem of elasticity theory to determine the background stress in the lithosphere. By sequentially selecting the boundary stresses and varying the physical elasticity parameters, we have constructed the stages of crustal stresses conforming to their empirically known values. The earthquake source is simulated in kinematic dislocation with subdivision into types: a concentrated dipole with a moment (type I), a concentrated double dipole without a moment (type II), and a singular volume. The numerical results of the model have shown that that the variations in stresses caused by a strong earthquake are largely determined by the proximity of orientation of displacement of the strong earthquake source and the axes of crustal structures affected by wave perturbation. In regions where stresses in the crust are close to critical, the stress increment can trigger seismic activation. [ABSTRACT FROM AUTHOR]